A known spice mill has two separate spice containers which can receive different spices, for example peppercorns and salt crystals. A grinding mechanism is provided at the bottom of each spice container to crush the spices. Each grinding mechanism is operably connected to a gear mechanism via a shaft having a gear wheel. One known gear mechanism includes a pivotable gear wheel which enters into engagement with the gear wheel on one shaft when the gear mechanism is driven in one direction and enters into engagement with the gear wheel of the other shaft when the gear mechanism is driven in the opposite direction. The containers are upwardly sealed by a covering which can be opened in order to add spices to the spice containers. Located above and separate from the covering is a rotary handle which can be rotated manually and drives the gear mechanism via a central shaft extending through the covering.